14x^2-92x+78=0

Solution for 14x^2-92x+78=0 equation:

Simplifying
14x2 + -92x + 78 = 0

Reorder the terms:
78 + -92x + 14x2 = 0

Solving
78 + -92x + 14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(39 + -46x + 7x2) = 0

Factor a trinomial.
2((1 + -1x)(39 + -7x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Subproblem 2
Set the factor '(39 + -7x)' equal to zero and attempt to solve:

Simplifying
39 + -7x = 0

Solving
39 + -7x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-39' to each side of the equation.
39 + -39 + -7x = 0 + -39

Combine like terms: 39 + -39 = 0
0 + -7x = 0 + -39
-7x = 0 + -39

Combine like terms: 0 + -39 = -39
-7x = -39

Divide each side by '-7'.
x = 5.571428571

Simplifying
x = 5.571428571
Solution
x = {1, 5.571428571}